---
id: 5900f3b01000cf542c50fec3
title: 'Problem 68: Magic 5-gon ring'
challengeType: 1
forumTopicId: 302180
dashedName: problem-68-magic-5-gon-ring
---

# --description--

Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine.

<img class="img-responsive center-block" alt="a completed example of a 3-gon ring" src="https://cdn-media-1.freecodecamp.org/project-euler/3-gon-ring.png" style="background-color: white; padding: 10px;" />

Working **clockwise**, and starting from the group of three with the numerically lowest external node (4,3,2 in this example), each solution can be described uniquely. 例如，上述解決方案可以通過集合來描述：4,3,2; 6,2,1; 5,1,3。

It is possible to complete the ring with four different totals: 9, 10, 11, and 12. There are eight solutions in total.

<div style='text-align: center;'>

| <div style='width: 100px;'>Total</div> | <div style='width: 250px;'>Solution Set</div> |
| -------------------------------------- | --------------------------------------------- |
| 9                                      | 4,2,3; 5,3,1; 6,1,2                           |
| 9                                      | 4,3,2; 6,2,1; 5,1,3                           |
| 10                                     | 2,3,5; 4,5,1; 6,1,3                           |
| 10                                     | 2,5,3; 6,3,1; 4,1,5                           |
| 11                                     | 1,4,6; 3,6,2; 5,2,4                           |
| 11                                     | 1,6,4; 5,4,2; 3,2,6                           |
| 12                                     | 1,5,6; 2,6,4; 3,4,5                           |
| 12                                     | 1,6,5; 3,5,4; 2,4,6                           |

</div>

By concatenating each group it is possible to form 9-digit strings; the maximum string for a 3-gon ring is 432621513.

Using the numbers 1 to 10, and depending on arrangements, it is possible to form 16- and 17-digit strings. What is the maximum **16-digit** string for a "magic" 5-gon ring?

<img class="img-responsive center-block" alt="a blank diagram of a 5-gon ring" src="https://cdn-media-1.freecodecamp.org/project-euler/5-gon-ring.png" style="background-color: white; padding: 10px;" />

# --hints--

`magic5GonRing()` should return a number.

```js
assert(typeof magic5GonRing() === 'number');
```

`magic5GonRing()` should return 6531031914842725.

```js
assert.strictEqual(magic5GonRing(), 6531031914842725);
```

# --seed--

## --seed-contents--

```js
function magic5GonRing() {

  return true;
}

magic5GonRing();
```

# --solutions--

```js
// solution required
```
